a. Let where a is a real number. Evaluate I(a) and show that its value is independent

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a. Let dx I(a) (1 + xª)(1 + x²)’ 18 ||  where a is a real number. Evaluate I(a) and show that its value is independent of a. Split the integral into two integrals over [0, 1] and [1, ∞]; then use a change of variables to convert the second integral into an integral over [0, 1].)

b. Let f be any positive continuous function on [0, π/2]. Evaluate 7/2 f(cos x) -dx. Jo f(cos x) + f(sin x)

Use the identity cos (π/2 - x) = sin x.)

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Calculus Early Transcendentals

ISBN: 978-0321947345

2nd edition

Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

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